/*
 * Unique Paths
A robot is located at the top-left corner of a m x n grid (marked 'Start' in the diagram below).

The robot can only move either down or right at any point in time. The robot is trying to reach the bottom-right corner of the grid (marked 'Finish' in the diagram below).

How many possible unique paths are there?
 */
package com.xinpan.exercise;

public class UniquePaths {
    public int uniquePaths(int m, int n) {
        // Start typing your Java solution below
        // DO NOT write main() function
        int[][] map = new int[m][n];
        for(int i = 0; i < m; i++)
            map[i][0] = 1;
        for(int i = 0; i < n; i++)
            map[0][i] = 1;
        
        for(int i = 1; i < m; i++)
        {
            for(int j = 1; j < n; j++)
            {
                map[i][j] = map[i-1][j] + map[i][j-1];
            }
        }
        return map[m-1][n-1];
    }
}
